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Consider the Diophantine equation:

$10^n-a^3-b^3=c^2$, for $a$, $b$, $c$, and $n$ positive.

Has this equation infinitely many solutions?

What if we add the restriction that a, b and c must not be multiple of 10 and greater than 2?

Consider the Diophantine equation:

$10^n-a^3-b^3=c^2$, for $a$, $b$, $c$, and $n$ positive.

Has this equation infinitely many solutions?

Consider the Diophantine equation:

$10^n-a^3-b^3=c^2$, for $a$, $b$, $c$, and $n$ positive.

Has this equation infinitely many solutions?

Consider the Diophantine equation:

$10^n-a^3-b^3=c^2$, for $a$, $b$, $c$, and $n$ positive.

Has this equation infinitely many solutions?

What if we add the restriction that a, b and c must not be multiple of 10 and greater than 2?